In the general population, 9 out of every 100 people will develop type 2 diabetes. 1 in 600 US adults carries a gene that makes them more susceptible to developing type 2 diabetes. 8 out 10 people who carry this gene develop type 2 diabetes. Show your work and use the correct probability notation. 5. Calculate the probability that a randomly selected US adult will develop type 2 diabetes given that they have the gene. 6. Calculate the probability that a randomly selected US adult carries the gene and develops type 2 diabetes. 7. Are the events of carrying the gene and developing type 2 diabetes independent? Explain